The Shape of Advertising Response Functions Revisited: A Model of Dynamic Probabilistic Thresholds
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Prior work in marketing has suggested that advertising threshold effects—levels beneath which there is essentially no sales response—are rarely encountered in practice. Because advertising policies settle into effective ranges through early trial and error, thresholds cannot be observed directly, and arguments for their existence must be based primarily on a "statistical footprint," that is, on relative fits of a range of model types. To detect possible threshold effects, we formulate a switching regression model with two "regimes," in only one of which advertising is effective. Mediating the switch between the two regimes is a logistic function of category-specific dynamic variables (e.g., order of entry, time in market, number of competitors) and advertising levels, nesting a variety of alternative formulations, among them both standard concave and S-shaped responses. A sequence of comparisons among parametrically related models strongly suggests: that threshold effects exist; that market share response to advertising is not necessarily globally concave; that superior fit cannot be attributed to model flexibility alone; and that dynamic, environmental, competitive, and brand-specific factors can influence advertising effectiveness. These effects are evident in two evolving durables categories (SUVs and minivans), although not in the one mature, nondurable category (liquid detergent) studied.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it